The Many-Worlds Calculus: Representing Quantum Control

Kostia Chardonnet (1, 2, 3) , Marc de Visme (1, 2) , Benoît Valiron (1, 2, 4) , Renaud Vilmart (1, 2)

1 LMF - Laboratoire Méthodes Formelles
2 QuaCS - Quantum Computation Structures
3 IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale
4 CentraleSupélec

We propose a new typed graphical language for quantum computation, based on compact categories with biproducts. Our language generalizes existing approaches such as ZX-calculus and quantum circuits, while offering a natural framework to support quantum control: it natively supports "quantum tests". The language comes equipped with a denotational semantics based on linear applications, and an equational theory. Through the use of normal forms for the diagrams, we prove the language to be universal, and the equational theory to be complete with respect to the semantics.

Keywords: Quantum Control; Graphical Languages; Linear Logic; Geometry of Interaction

Domains: Quantum Physics [quant-ph]; Logic in Computer Science [cs.LO]

Kostia Chardonnet, Marc de Visme, Benoît Valiron, Renaud Vilmart. The Many-Worlds Calculus: Representing Quantum Control. 2022. ⟨hal-03654190v1⟩